Exploring the exact soliton solutions, stability, and modulation instability analysis to the Wu-Zhang water wave model

In this research, we reveal the impressive exact solitons to the space–time fractional Wu-Zhang model. This model describes the nonlinear water waves availability and harbor and coastal design in engineering fields. For this investigation, we utilized the novel technique, the Sardar sub-equation scheme. We obtained various wave solutions containing trigonometric, hyperbolic and rational profiles. Dynamical description of the gained solutions is provided through two-D, three-D and contour graphs. Further, stability is checked by applying stability analysis. Additionally, steady-state results are gained by using modulation instability. Non-linear optics, engineering, fluid physics, oceanography and many other domains can benefit from the obtained results. It is concluded that the used technique is also helpful for other nonlinear fractional models.